Question

factor completely. (-2x^{4}+20x^{3}+48x^{2})

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the terms. The GCF of $-2x^{4}$, $20x^{3}$, and $48x^{2}$ is $-2x^{2}$.
$-2x^{4}+20x^{3}+48x^{2}=-2x^{2}(x^{2} - 10x - 24)$

Step2: Factor the quadratic expression

Factor the quadratic $x^{2}-10x - 24$. We need to find two numbers that multiply to $-24$ and add up to $-10$. The numbers are $-12$ and $2$.
$x^{2}-10x - 24=(x - 12)(x+2)$

Answer:

$-2x^{2}(x - 12)(x + 2)$